Solve: Product of Square Roots (√2 × √6 × √12) ÷ √16

Solve the following exercise:

$\frac{\sqrt{2}\cdot\sqrt{6}\cdot\sqrt{12}}{\sqrt{16}}=$

Video Solution

Solution Steps

00:00 Solve the following problem

00:03 When multiplying the square root of a number (A) by the square root of another number (B)

00:06 The result equals the square root of their product (A times B)

00:10 Apply this formula to our exercise and calculate the multiplication

00:38 The square root of the numerator (A) divided by square root of the denominator (B)

00:43 Equals the square root of the entire fraction (A divided by B)

00:46 Apply this formula to our exercise

00:54 Calculate 144 divided by 16

00:58 Break down 9 to 3 squared

01:01 This is the solution

Step-by-Step Solution

To solve this problem, we'll use the properties of square roots:

Step 1: Apply the multiplication property of square roots in the numerator:
$\sqrt{2} \cdot \sqrt{6} \cdot \sqrt{12} = \sqrt{2 \cdot 6 \cdot 12}$
Step 2: Calculate the product under the square root:
$2 \cdot 6 \cdot 12 = 144$
Step 3: Combine the expression:
$\frac{\sqrt{144}}{\sqrt{16}}$
Step 4: Simplify the square roots:
$\sqrt{144} = 12$ and $\sqrt{16} = 4$
Step 5: Use the properties of the quotient of square roots:
$\frac{12}{4} = 3$

Thus, the final simplified expression is $\mathbf{3}$ .